Efficient searching with linear constraints

Journal of Computer and System Sciences

Volumn 61, Issue 2, 2000, Pages 194-216

  Agarwal, Pankaj K ^a   Arge, Lars ^a   Erickson, Jeff ^b   Franciosa, Paulo G ^c   Vitter, Jeffrey Scott ^a  

^a Duke University   (United States)

^b University of Illinois at Urbana Champaign   (United States)

^c SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

DATA STORAGE EQUIPMENT; DATA STRUCTURES; DATABASE SYSTEMS; ONLINE SEARCHING;

HALFSPACE RANGE SEARCHING; LINEAR CONSTRAINT QUERIES;

CONSTRAINT THEORY;

EID: 0034295416     PISSN: 00220000     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcss.2000.1709     Document Type: Article

References (53)

1. P. K. Agarwal, L. Arge, J. Erickson, P. G. Franciosa, and J. S. Vitter, Efficient searching with linear constraints, in Proc. 17th Annu. ACM Sympos. Principles Database Syst., 1998, pp. 169-178.
2. Agarwal P. K., Aronov B., Chan T. M., Sharir M. On levels in arrangements of lines, segments, planes, and triangles. Discrete Comput. Geom. 19:1998;315-331.
3. Agarwal P. K., Erickson J. Geometric range searching and its relatives. Chazelle B., Goodman J. E., Pollack R. Advances in Discrete and Computational Geometry. 1999;1-58 AMS Press, Providence.
4. Agarwal P. K., van Kreveld M., Overmars M. Intersection queries in curved objects. J. Algorithms. 15:1993;229-266.
5. L. Arge and J. S. Vitter, Optimal dynamic interval management in external memory, in Proc. IEEE Symp. on Foundtions of Comp. Sci., 1996, pp. 560-569.
6. Arge L., Samoladas V., Vitter J. S. On two-dimensional indexability and optimal range search indexing. Proc. ACM Symp. Principles of Database Systems. 1999;. p. 346-357.
7. L. Arge, D. E. Vengroff, and, J. S. Vitter, External-memory algorithms for processing line segments in Geographic Information Systems, Algorithmica, to appear. An extended abstract appears in "Proc. of Third European Symposium on Algorithms, 1995."
8. Bayer R., McCreight E. Organization and maintenance of large ordered indexes. Acta Inform. 1:1972;173-189.
9. N. Beckmann, H.-P. Kriegel, R. Schneider, and B. Seeger, The R*-tree: An efficient and robust access method for points and rectangles, in Proc. SIGMOD Intl. Conf. on Management of Data, 1990, pp. 322-331.
10. S. Berchtold, D. A. Keim, and H.-P. Kriegel, the X-tree: An index structure for higher dimensional data, in Proc. 22th VLDB Conference, 1996, pp. 28-39.
11. T. M. Chan, Random sampling, halfspace range reporting, and construction of (≤k)-levels in three dimensions, in Proc. 39th IEEE Symp. Foundations of Computer Science, 1998, pp. 586-595.
12. Chazelle B. Filtering search: a new approach to query-answering. SIAM J. Comput. 15:1986;703-724.
13. Chazelle B., Cole R., Preparata F. P., Yap C. K. New upper bounds for neighbor searching. Inform. Control. 68:1986;105-124.
14. Chazelle B., Guibas L. J., Lee D. T. The power of geometric duality. BIT. 25:1985;76-90.
15. Chazelle B., Preparata F. P. Halfspace range search: An algorithmic application of k-sets. Discrete Comput. Geom. 1:1986;83-93.
16. Clarkson K. L., Shor P. W. Applications of random sampling in computational geometry, II. Discrete Comput. Geom. 4:1989;387-421.
17. Comer D. The ubiquitous B-tree. ACM Comput. Surveys. 11:1979;121-137.
18. A. Crauser, P. Ferragina, K. Mehlhorn, U. Meyer, and E. Ramos, Randomized external-memory algorithms for some geometric problems, in Proc. 14th Annu. ACM Sympos. Comput. Geom., 1998, pp. 269-268.
19. Dey T. K. Improved bounds on planar k-sets and related problems. Discrete Comput. Geom. 19:1998;373-382.
20. F. Dumortier, M. Gyssens, and L. Vandeurzen, On the decidability of semi-linearity for semi-algebraic sets and its implications for spatial databases, in Proc. ACM Symp. Principles of Database Systems, 1997, pp. 68-77.
21. Edelsbrunner H. Algortihms in Combinatorial Geometry. 1987;Springer-Verlag, Heidelberg.
22. Edelsbrunner H., Welzl E. Constructing belts in two-dimensional arrangements with applications. SIAM J. Comput. 15:1986;271-284.
23. Π-tree: a multi-attribute index supporting concurrency, recovery and node consolidation. VLDB J. 6:1997;1-25.
24. P. G. Franciosa, and, M. Talamo, Time optimal halfplane search on external memory, Unpublished manuscript, 1997.
25. Franciosa P. G., Talamo M. Orders, k-sets and fast halfplane search on paged memory. Proc. Workshop on Orders, Algorithms and Applications. Lecture Notes in Computer Science. 831:1994;Springer-Verlag, Berlin/New York. p. 117-127.
26. J. Goldstein, R. Ramakrishnan, U. shaft, and J.-B. Yu, Processing queries by linear constraints, in Proc. ACM Symp. Principles of Database Systems, 1997, pp. 257-267.
27. M. T. Goodrich, J.-J. Tsay, D. E. Vengroff, and J. S. Vitter, External-memory computational geometry, in Proc. IEEE Symp. on Foundations of Comp. Sci., 1993, pp. 714-723.
28. Güting R. H. An introduction to spatial database systems. VLDB J. 4:1994;357-399.
29. A. Guttman, R-trees: A dynamic index structure for spatial searching, in Proc. SIGMOD Intl. Conf. on Management of Data, 1985, pp. 47-57.
30. Haussler D., Welzl E. Epsilon-nets and simplex range queries. Discrete Comput. Geom. 2:1987;127-151.
31. A. Henrich, Improving the performance of multi-dimensional access structures based on kd-trees, in Proc. 12th IEEE Intl. Conf. on Data Engineering, 1996, pp. 68-74.
32. E. G. Hoel and H. Samet, A qualitative comparison study of data structures for large line segment databases, in Proc. ACM SIGMOD Conf. on Management of Data, 1992, pp. 205-214.
33. I. Kamel and C. Faloutsos, Hilbert R-tree: An improved R-tree using fractals, in Proceedings 20th International Conference on Very Large Databases, 1994, pp. 500-509.
34. Kanellakis P. C., Ramaswamy S., Vengroff D. E., Vitter J. S. Indexing for data models with constraints and classes. J. Comput. System. Sci. 52:1996;589-612.
35. Lomet D., Salzberg B. The hB-tree: A multiattribute indexing method with good guaranteed performance. ACM Trans. Database Systems. 15:1990;625-658.
36. Matousek J. Efficient partition trees. Discrete Comput. Geom. 8:1992;315-334.
37. Matousek J. Reporting points in halfspaces. Comput. Geom. Theory Appl. 2:1992;169-186.
38. Matousek J. Geometric range searching. ACM Comput. Surv. 26:1994;421-461.
39. Mehlhorn K. Multi-dimensional Searching and Computational Geometry. 1984;Springer-Verlag, Heidelberg.
40. Motwani R., Raghavan P. Randomized Algorithms. 1995;Cambridge University Press, New York.
41. Nievergelt J., Hinterberger H., Sevcik K. The grid file: An adaptable, symmetric multikey file structure. ACM Trans. Database Systems. 9:1984;257-276.
42. Nievergelt J., Widmayer P. Spatial data structures: Concepts and design choices. van Kreveld M., Nievergelt J., Roos T., Widmayer P. Algorithmic Foundations of GIS. Lecture Notes in Computer Science. 1340:1997;Springer-Verlag, Berlin/New York.
43. Overmars M. H., van Leeuwen J. Maintenance of configurations in the plane. J. Comput. System Sci. 23:1981;166-204.
44. S. Ramaswamy and S. Subramanian, Path caching: A technique for optimal external searching, in Proc. ACM Symp. Principles of Database Systems, 1994, pp. 25-35.
45. J. Robinson, The K-D-B tree: A search structure for large multidimensional dynamic indexes, in Proc. ACM SIGMOD Conf. on Management of Data, 1984, pp. 10-18.
46. Samet H. Applications of Spatial Data Structures: Computer Graphics, Image Processing, and GIS. 1989;Addison-Wesley, Reading.
47. Samet H. The Design and Analysis of Spatial Data Structures. 1989;Addison-Wesley, Reading.
48. +-tree: A dynamic index for multi-dimensional objects, in, Proc. IEEE International Conf. on Very Large Databases, 1987.
49. S. Subramanian and S. Ramaswamy, The P-range tree: A new data structure for range searching in secondary memory, in Proc. ACM-SIAM Symp. on Discrete Algorithms, 1995, pp. 378-387.
50. G. Tóth, Point sets with many k-sets, in preparation.
51. D. E. Vengroff and J. S. Vitter, Efficient 3-d range searching in external memory, in Proc. ACM Symp. on Theory of Computation, 1996, pp. 192-201.
52. J. S. Vitter, Online data structures in external memory, in, Proc. Annual International Colloquim on Automata, Languages, and Programming, 1999.
53. Willard D. E. Polygon retrieval. SIAM J. Comput. 11:1982;149-165.